Following McGregor's victory, which took just 40 seconds, Mayweather – who stopped the UFC star in the 10th round on his professional boxing debut in August 2017 – teased a second bout for later this year.
In a post uploaded to his official Instagram account, Mayweather tagged a picture of a mock-up poster with the caption: "Mayweather McGregor 2, 2020".
UFC boss Dana White also suggested something was in the works with Mayweather and, after making his long-awaited comeback to the Octagon, McGregor seemed adamant a rematch would go ahead.
"Yes, he forgot McGregor Sports & Entertainment off the poster, so that cuts him out, it’s going to be me and Manny [Pacquiao]," joked McGregor in a news conference.
"We'll see what happens. He's a funny man, old Floyd, but the discussions never stop. You know Floyd, he goes through money, and fast, so he's far from retired.
"That rematch will happen at some stage.
"I've been getting great training in with the team back home. I'm an experienced fighter, I've done it all and can do it all. As long as I'm fit, we'll see what presents itself."
McGregor had not fought since a defeat to Khabib Nurmagomedov in October 2018, but the 31-year-old would relish the opportunity to take on the Russian again, especially in Moscow.
"It's got very personal with that man and his team," McGregor said. "I am who I am, it is what it is. I'd be excited to get that one back but we'll see what happens. If something happens, I'll be here.
"There's a lot of money in Russia, a lot of revenue. I love Russia and the people, I went to Moscow recently and they're so passionate about the sport of mixed martial arts and so passionate about myself.
"What a place, it'd be like something out of a Rocky movie, so I'd be very eager. I want to create spectacles for the people, it's one hell of a spectacle. When I went out there last time, the world stopped. I would love to compete there."
McGregor was also asked if he would consider a stadium fight in Europe and insisted Dublin would be the only city a possible bout would take place in.
"If there's a stadium show happening in Europe, then it's happening in Ireland, not the UK," he said.
"If there's a stadium show earmarked for me in Europe, bring that to Ireland, I've been asking that since the beginning. I'd love to compete in my hometown."